Читать книгу Physics I For Dummies - Steven Holzner - Страница 64

Here’s an acceleration example. As they strap you into the jet on the aircraft carrier deck, the mechanic says you need to take off at a speed of at least 62.0 m/s. You’ll be catapulted at an acceleration of 31 m/s². Is there going to be enough catapult to do the job? You ask how long the catapult is. “A hundred meters,” says the mechanic, finishing strapping you in.

Hmm, you think. Will an acceleration of 31 m/s² over a distance of 100 meters do the trick? You take out your clipboard and ask yourself: How far must I be accelerated at 31 m/s² to achieve a speed of 62 m/s?

First think of the distance that you need to be accelerated over as the size of the displacement from your initial position. To find this displacement, you can use the equation , where s is the displacement, is the average velocity, and t is the time — which means you have to find the time over which you’re accelerated. For that, you can use the equation that relates change in velocity, , acceleration a, and change in time, :

Solving for gives you

Plugging in the numbers and solving gives you the change in time:

Okay, so it takes 2.0 seconds for you to reach a speed of 62 m/s if your rate of acceleration is 31 m/s². Now you can use this equation to find the total distance you need to travel to get up to this speed; it is the size of the displacement, which is given by , where , , and . So your equation is

Plugging in the numbers gives you

So it will take 62 meters of 31 m/s² acceleration to get you to takeoff speed — and the catapult is 100 meters long. No problem.